In a small saucepan, combine the quinoa with 2 cups of water and the salt. Bring to a simmer, reduce heat to low, cover and cook for 12 minutes. Cool slightly, then toss with the tomatoes, green onions, kalamata olives, red onion, parsley, lemon juice, and oil.
Meanwhile, make the pesto. Combine all of the ingredients except the oil in a blender, food processor, or immersion blender. Process until mostly smooth. With the motor running, slowly add the oil until you reach a smooth and creamy consistency. It is important that you add the oil slowly and not all at once. Season to taste.
Preheat your indoor or outdoor grill to medium.
Season the salmon fillets with salt and pepper. Place the fish on the grill skin side up for 5 minutes. Flip and grill for another 5 minutes. The internal temperature of the salmon will be 115°F at medium rare. If you prefer your salmon more well done just leave it on the grill another 1-2 minutes per side.
To serve, divide the quinoa salad between bowls with salmon fillets on top. Garnish with baby arugula and serve with the basil pesto.